Now, this isn’t the best way to maximize expected value. If you were an expected value maximizing robot, you would not pursue this strategy. You would say “bleep bloop, this brings about 93.5 fewer expected utils than the other strategy.” But I assume you are not an EV maximizing robot.
Hmmm. This is interesting, as diversification is expected utility maximizing in the finance context. The fact that it is not EV maximizing in the utilitarian framework makes me wonder if there is something wrong with the framing.
The obvious difference is that EV is risk-neutral. I think this is usually justified by the fact that we are counting utils, whereas in finance, we are counting dollars. Arguably, it makes sense that utility is concave in dollars, but not that utility is (strictly) concave in itself.
Intuitively, this seems wrong to me. Imagine a choice set {A, B}. Choice A has a 50% chance of resulting in a world with 1 million sentient beings, all with 100 utils each, and a 50% chance of resulting in a world with zero sentient beings. Choice B results with certainty in a world with 500 thousand sentient beings, all with 100 utils each. I strictly prefer Choice B to Choice A, implying that I have a moral meta utility function that is concave in utils. This is sufficient to derive that diversification is optimal.
Feels like the most straightforwardly rational argument for portfolio diversification is the assumption your EV and probability estimates almost certainly aren’t the accurate or at least unbiased estimator they need to be for the optimal strategy to be to stick everything on the highest EV outcome. Even more so when the probability that a given EV estimate is accurate is unlikely to be uncorrelated with whether it scores particularly highly (the good old optimiser’s curse, with a dose of wishful thinking thrown in). Financiers don’t trust themselves to be perfectly impartial about stuff like commodity prices in central Asia or binary bets on the value of Yen on Thursday, and it seems unlikely that people who are extremely passionate about the causes they and their friends participate in ahead of a vast range of other causes that nominally claim to do good achieve a greater level of impartiality. Pascalian odds seem particularly unlikely to be representative of the true best option (in plain English, a 0.0001% subjective probability assessment of a 1 shot event is roughly “I don’t really know what the outcome of this will be and it seems like there could be many, many things more likely to achieve the same end”). You can make the assumption that if they appear to be robustly positive and neglected they might deserve funding anyway, but that is a portfolio argument...
Hmmm. This is interesting, as diversification is expected utility maximizing in the finance context. The fact that it is not EV maximizing in the utilitarian framework makes me wonder if there is something wrong with the framing.
The obvious difference is that EV is risk-neutral. I think this is usually justified by the fact that we are counting utils, whereas in finance, we are counting dollars. Arguably, it makes sense that utility is concave in dollars, but not that utility is (strictly) concave in itself.
Intuitively, this seems wrong to me. Imagine a choice set {A, B}. Choice A has a 50% chance of resulting in a world with 1 million sentient beings, all with 100 utils each, and a 50% chance of resulting in a world with zero sentient beings. Choice B results with certainty in a world with 500 thousand sentient beings, all with 100 utils each. I strictly prefer Choice B to Choice A, implying that I have a moral meta utility function that is concave in utils. This is sufficient to derive that diversification is optimal.
Feels like the most straightforwardly rational argument for portfolio diversification is the assumption your EV and probability estimates almost certainly aren’t the accurate or at least unbiased estimator they need to be for the optimal strategy to be to stick everything on the highest EV outcome. Even more so when the probability that a given EV estimate is accurate is unlikely to be uncorrelated with whether it scores particularly highly (the good old optimiser’s curse, with a dose of wishful thinking thrown in). Financiers don’t trust themselves to be perfectly impartial about stuff like commodity prices in central Asia or binary bets on the value of Yen on Thursday, and it seems unlikely that people who are extremely passionate about the causes they and their friends participate in ahead of a vast range of other causes that nominally claim to do good achieve a greater level of impartiality. Pascalian odds seem particularly unlikely to be representative of the true best option (in plain English, a 0.0001% subjective probability assessment of a 1 shot event is roughly “I don’t really know what the outcome of this will be and it seems like there could be many, many things more likely to achieve the same end”). You can make the assumption that if they appear to be robustly positive and neglected they might deserve funding anyway, but that is a portfolio argument...
Interesting point, though I disagree—I think there are strong arguments for thinking that you should just maximize utility https://joecarlsmith.com/2022/03/16/on-expected-utility-part-1-skyscrapers-and-madmen/